Limit of function sin ( pi / x ) as x goes to zero

[grapz]

Lim x --> 0 sin ( pi / x )

I know it oscillates between 1 and -1 and thus it has no limit, but i don't understand why. Can someone go through the steps with me and show me why that is for this graph.

thx

 

[tkhunny]

It oscillates faster and faster and faster. It doesn't quit oscillating.

As x approaches zero, 1/x increases without bound. What does the sine function do as it's agrument wanders off to the positive. Does it ever settle down? It just keeps oscillating.